Cloud computing is a new delivery model for IT services. Cloud platforms are being increasingly used for the deployment and execution of service-based business processes (SBPs). Nevertheless, the provisioning of elastic infrastructures and/or platforms is not sufficient to provide users with elasticity at the level of SBPs. Therefore, there is a need to provide SBPs with mechanisms to scale their resource requirements up and down whenever possible. This can be achieved using mechanisms for duplicating and consolidating business services that compose the SBPs. In this paper, we propose a formal model for SBPs elasticity in the Cloud. We show that our model preserves the semantics of SBPs when services are duplicated or consolidated. We also propose a formal framework for the evaluation of elasticity strategies that decide on when and how many resources are required to ensure elasticity of SBPs.